2.1.2.1 MRI as an Ionizing Radiation‐free Imaging Method

During the 1970s, there have been several imaging methods used in research and clinical investigation, including CT and positron emission tomography (PET). Among the variety of imaging methods, MRI has quickly gathered attention because it can reveal different types of brain tissues based on the physical properties of body composition (e.g. the content of water molecules) as a ‘natural’ contrast agent. The non‐contrast MRI (which does not require an injection of extra radioactive agents) is a method free of ionizing radiation. In contrast, CT is a method based on the use of X‐ray, and PET requires injecting radionuclides as the ‘tracers’ for contrasting body tissue. From an experimental perspective, because the risk of ionizing radiation can be minimized for the volunteers, MRI is useful for repeated scans of several sessions or longitudinal follow‐up, thus becoming a mainstream method for clinical research (Lin and Yeung 2020).

2.1.2.2 Using Intrinsic Contrast for Functional Neuroimaging

Over the past 30 years, coupled with the emergence of cognitive neuroscience, there has been an increasing demand for using biomedical imaging to explore brain functions (Raichle 2009). Various methods have been developed for functional neuroimaging, which aims to ‘localize different mental processes to different parts of the brain, in effect creating a map of which areas are responsible for which processes’. (Huettel et al. 2004). To achieve the ‘functional mapping’ of the brain, a critical condition is to detect the signal change coupled with the change of neural activity. A great advantage of functional magnetic resonance imaging (fMRI), compared to the methods (e.g. PET), is that it can detect such a signal change without the help of external contrast media. The signal measured by fMRI is the BOLD signal, which indirectly relates to neural activity, with the following mechanisms. Home buyers are wonderful for fast-selling homeowners since they’ll purchase any property. Visit https://www.ibuyers.app/rhode-island/.

Firstly, the brain region with increased neural activity is associated with more energy consumption, i.e. increased level of synaptic activity. The consumption of oxygen is associated with increased cerebral blood flow (CBF) and changes in cerebral vessel volume, leading to an over‐supply of the oxygenated vs. deoxygenated haemoglobin. The association between changes in haemodynamic response and changes in neural activity, namely neurovascular coupling, has been investigated for more than 100 years (Roy and Sherrington 1890) (Figure 2.1). Secondly, Thulborn et al. (1982) found that deoxygenated haemoglobin increased the magnetic susceptibility. A lower signal from MRI was found when blood was highly deoxygenated. In other words, one can estimate the change in deoxygenated haemoglobin by measuring the change in MR signals. Furthermore, Ogawa et al. (1990a,b) demonstrated that blood oxygen could be an intrinsic agent for contrasting the different conditions of metabolic demand or blood flow of the brain. They found that the MR signals will increase and decrease according to the level of oxygenated and deoxygenated haemoglobin, and this change is associated with a complex haemodynamic process, such as changes in CBF and cerebral blood volume (Huettel et al. 2004) (Figure 2.1 and Box 2.1). Simply speaking, fMRI detects the metabolic changes in the proportion of deoxygenated and oxygenated haemoglobin in the brain via changes in BOLD signals, which is further influenced by a complicated haemodynamic process (for further discussion of the mechanism issues, see Section 2.1.4). In fMRI, brain mapping of mental functions is indirectly inferred from the local change of the BOLD signal, which reflects the metabolic changes related to neural activity.

2.2.2.1 What Is the ‘Task’ for Task‐based Functional Neuroimaging?

It is always crucial to elucidate the details of the task design because a slight difference between the two tasks may result in different mental functions, and thus very different patterns of brain activation. For example, if a task requires subjects to chew a piece of gum for five minutes continuously, the subjects may gradually feel bored and uncomfortable, and it becomes possible that the acquired BOLD signals reflect not only chewing movement but also the change in subjects’ emotional status. Therefore, in most of the studies, a period of chewing is often followed by a resting period so that subjects may not develop fatigue or distress. However, researchers need to further remind subjects to resume chewing after the resting period, usually by an auditory or a visual cue. The use of sensory cues may introduce an additional auditory or visual experience, which is further associated with brain activation related to auditory or visual processing. The examples here highlight the importance of a clear definition of a task condition in neuroimaging research. The key issue for interpreting the neuroimaging results is to clarify what subjects actually do during a task and what mental functions are engaged within the task.

2.2.2.2 What Is the Baseline Condition Used for Control?

It is intuitive to think that the BOLD signals collected when a subject is performing some task must be task‐related. This is partially correct because not all the signals acquired during the task condition are task‐specific. In fact, most of the signals can be irrelevant to the task because there are some undergoing mental activities that are not specifically linked to the task. For example, during a chewing task, subjects may continuously pay attention to a visual cue that guides the task procedure. Such a baseline brain activity of sustained visual attention is not specifically associated with chewing. Therefore, a condition for controlling the baseline activity is usually necessary. As shown in Figure 2.2, most of the chewing tasks were contrasted to a control task in which subjects were instructed to rest (i.e. not chewing). The contrast between chewing vs. not chewing may reflect different conditions in jaw movement. However, the two conditions also differ in the degree of sensory processing because subjects may not have any teeth contacted during the baseline (resting) condition. Therefore, brain activation may be associated with both sensory and motor processing during chewing. If subjects are asked to occlude their teeth during the baseline condition, the contrast may be more specifically related to motor control because the sensory factor is better balanced between the task and the baseline condition. In other words, the definition of the baseline condition plays a key role in interpreting neuroimaging results because it reflects the factors being controlled when the mental function of interest is contrasted.

2.2.2.3 Practical Issues of a Task‐based Study

In the preceding sections, we have highlighted the importance of defining both the task and the baseline conditions with clarity. To most neuroimaging researchers, to conceive a perfect plan of these designs is just the first step for their success. A greater challenge comes from a very practical issue: all the designs need to be carried out while subjects are receiving a scan. This is especially challenging to fMRI because all the tasks need to be performed inside an MRI scanner, which may be a sub‐optimal condition of performing a behavioural task due to the confined space and restriction of using ferromagnetic materials. Again, we use the chewing study as an example to demonstrate these practical challenges. Firstly, when receiving the scan, the head of the subjects is positioned inside a head coil that transmits and receives the radiofrequency signal of MRI. During scanning, subjects can still move their jaws, but the jaw movement is restricted to the head coil. Therefore, the jaw movement of an fMRI chewing task can be different from the movement during eating. In other words, the external validity of neuroimaging results may be compromised because the ‘chewing task’ does not perfectly mimic real chewing. Secondly, chewing is associated with saliva secretion, and how should we evaluate the effect of saliva swallowing on the observed BOLD signals? One may just instruct subjects ‘not to swallow your saliva while chewing a gum’. However, such instruction is very difficult for subjects to follow. The compliance of subjects to task instruction is a crucial factor of the study. Some of these challenges can be tackled with external assessment, such as tracking jaw movement of swallowing during an fMRI scan. However, most of the electronic devices are not compatible with an MRI scanner, in which the use of ferromagnetic materials is restricted for safety reasons. In general, these practical issues should be carefully considered when experimental tasks are designed.

2.2.3.1 Inter‐subject Variability – The Behavioural Aspects

In the preceding discussion, we focused on the comparison between the task and the baseline conditions, which would reflect the mental functions we desire to investigate. The comparison is performed for an individual subject, i.e. the subject‐level or first‐level analysis of imaging data. To make an inference about group difference (e.g. differential activation between patient and control groups), the subject‐level results need to be synthesized, and a between‐group comparison will be performed, i.e. the group‐level or second‐level analysis (Figure 2.2). A critical issue of group‐level analysis is the inter‐subject variability. Many subject factors, such as sex, age, and health conditions, have a substantial association with brain structure and functions (Ruigrok et al. 2014; Lemaitre et al. 2012). For example, in a group of older subjects with a great age range, their brain activation related to a motor task may show greater variability. The variability may not just reflect the individual difference in motor processing, but also the difference in brain structure because brain atrophy is associated with increased age (Lemaitre et al. 2012). Therefore, a critical step to solve the problem is to clearly define the inclusion and exclusion criteria for recruiting subjects. The variability can be reduced by recruiting subjects with a higher homogeneity in terms of these factors (Figure 2.3a).

Secondly, inter‐subject variability may exist as a trait factor, like a personal disposition that influences one’s behaviour. This is particularly important for a task related to cognitive–affective processing, in which subjects’ performance is associated with their trait (i.e. dispositional factor) as well as the task per se (i.e. the situational factor). For example, in an fMRI study on pain modulation, subjects anticipated the pain intensity they would receive. It is not surprising that some subjects anticipated the pain to be milder and others anticipated it to be stronger (i.e. great variability in task results). The anticipatory process is not only associated with the sensory stimuli they received but also with individual differences in attention and imagination. The researchers found the subjective rating of pain anticipation and the activation of the brainstem, which plays a key role in modulating pain, were significantly correlated (Fairhurst et al. 2007). In this case, individual variability of task performance would be useful for providing an interpretation of variability in brain activation (Figure 2.3b).

2.2.3.2 Inter‐subject Variability – The Neuroimaging Aspects

As noted previously, the variability of brain structure and functions can be reduced by recruiting a group of subjects with a higher homogeneity. However, the problem is not fully solved because there is always a difference in the global architecture of the brain between individuals (Figure 2.3c). For example, a comparison of regional differences (e.g. the size of the hippocampus) will be invalid when there exists a great difference in the global morphology of individual brains. In fMRI, this problem is solved by a series of steps of imaging processing. The basic concept is to register the brain images of individual subjects to a template image of the brain, which is calculated by averaging brain images from a group of people. For example, the Montreal Neurological Institute (MNI) developed the MNI305 template, which is derived from the T1‐weighted structural images from healthy young adults (Evans et al. 2012). It is noteworthy that this template brain does not represent a brain of a real person. Instead, the template reflects an ‘on‐average brain’ estimated by statistical methods. The step to register each individual brain image to the template is spatial normalization. After normalization, the individual brain images are positioned in the same spatial format (i.e. the format of the template image), and then they can be compared.

Methodologically, brain images can be spatially transformed based on linear and nonlinear approaches. In linear transformation, two images are rotated and translated in the 3D space so that they can be overlapped. The original images are translated in the x‐, y‐ and z‐axes and rotated over the x‐, y‐ and z‐axes (i.e. the rigid transformation) (Figure 2.3c). Additionally, the image will be resized and sheared to match the template. In nonlinear transformation, the images will be locally warped to match with the template (Jenkinson and Chappell 2018). Notably, the nonlinear warping will lead to the deformation of the original image at the voxel level. For each voxel, local geometric changes will be recorded. Technical issues regarding the algorithms of imaging analysis are beyond the scope of the book. Nevertheless, it is critical to recognize that these procedures are crucial for analyzing neuroimaging data (see Box 2.3 in the Companion Website).

2.2.4.1 Statistical Analysis at the Individual Level

The individual‐level analysis aims to investigate the association between the BOLD signals and experiment conditions. Exactly speaking, the analysis focuses on the association between the time‐varying BOLD signals (i.e. time series) and the progression of a task. As shown in Figure 2.4a, an fMRI study of chewing may consist of four chewing blocks interleaved with four resting blocks. If the BOLD signal of a voxel is highly associated with the task, one should expect to see a strong association between the BOLD time series of the voxel and the task progression. The association can be quantified as the correlation between these two. In other words, the purpose of the first‐level analysis is to examine how the BOLD time series nicely fits the predicted BOLD response, which is derived from the task timing (Jenkinson and Chappell 2018). To achieve this goal, the general linear model (GLM) is widely used to estimate the coefficient of the fitting process. A greater coefficient of the GLM suggests a greater effect size of the fitting process, i.e. a stronger association between the BOLD time series of the voxel and the task (e.g. Voxel A in Figure 2.4a, compared to Voxel B). For a whole‐brain analysis, the GLM analyses will be performed for all the voxels within the whole brain for individual subjects. Therefore, by mapping the coefficients at the whole‐brain scale, one can identify the voxels or clusters of voxels that are associated with the task.

2.2.4.2 Statistical Analysis at the Group Level

The analysis at the individual level identifies the brain activation associated with the experimental conditions for each subject. The results reflect the association between mental functions (which is contrasted by a task and a baseline condition) and the BOLD time series of a voxel. The second‐level analysis, in contrast, aims to combine the individual results within a group. The group‐based analysis provides a great advantage for investigating clinical questions. For example, does the pattern of brain activation associated with chewing (derived from the individual‐level analysis) differ between TMD patients and healthy controls? To answer this question, the Student’s t‐test can be performed by comparing the brain activation between a group of TMD patients and a group of controls (Figure 2.4b). Notably, the ‘brain activation’ derived from the individual‐level analysis consists of the results from all the voxels in the brain. Therefore, in the case of a between‐group comparison, the t‐tests will be performed for each individual voxel. The result of the t‐tests (e.g. the t‐score) will be assigned to each voxel. Therefore, the group‐level analysis generates a new brain image, in which each voxel value represents the difference of brain activation (quantified by the t‐score) between two groups.

The same approach can be used to investigate the brain activation associated with individual differences. For example, do people with a better chewing function have higher activation in the motor cortex? To answer this question, regression analyses can be performed by investigating the association between brain activation and task performance (e.g. chewing performance) or individual factors (e.g. number of missing teeth). The association can be quantified by the beta coefficient of the regression model. The group‐level analysis can be performed at the whole‐brain scale (e.g. for all the voxels within the brain) and specifically for a region of interest (ROI). In the latter (i.e. an ROI‐based analysis), brain activation is analyzed specifically for the voxels within a pre‐defined ROI, which is usually selected based on a priori knowledge of brain functions (Poldrack 2007).

2.2.4.3 Statistical Thresholding for Imaging Results

The results from the group‐level analysis may already provide some useful information for research and clinical purposes. In the case of chewing research, we might obtain a brain map that shows the difference of chewing‐associated activation between groups (in which voxel intensity denotes a t‐score for between‐group comparison). The brain map may also present the strength of association between masticatory performance and chewing‐associated activation (in which voxel intensity denotes a regression coefficient). However, as for all research, we need to evaluate the Type I and Type II errors related to our results, which are associated with the risk of finding false‐positive and false‐negative results, respectively. For example, should we believe that a voxel with a very low t‐score really reflects a genuine between‐group difference? A practical way to control for these errors is to set a threshold for the imaging results. For example, a threshold of t‐score = 2 means that all the voxels with a t‐score > 2 will be considered ‘significant’ or ‘important’ (Figure 2.4c). In other words, we may set up a threshold to the intensity for each voxel, and only the voxels ‘survive’ under such a threshold will be taken for further interpretation (Figure 2.4c).

In addition to the approach of intensity‐based thresholding, the approach of cluster‐based thresholding aims to evaluate if the size of a cluster of voxels is large enough to be called significant or important. This is based on the assumption that, biologically, neurons work coherently for a mental function. For example, it may not be very convincing if painful stimulation is associated with the activation of just one single voxel in the sensory cortex (even though the ‘intensity’ of the activation is very high). It would be doubtful that such activation may be a ‘false positive’ one due to signal noise. In contrast, a cluster (i.e. spatially contiguous activation of voxels) with a larger size may be a more plausible result. The larger cluster suggests that all the voxels in the brain region would participate in pain processing (Figure 2.4c). Both thresholding approaches are widely used in neuroimaging research.

2.2.5.1 Considerations About the ‘Subtraction’ Design and Pure Insertion

The task‐based design is based on the assumption that mental functions can be contrasted by comparing between a task condition and a baseline condition. For example, the brain activation related to pain can be identified by contrasting the condition of ‘painful stimulation’ to the condition ‘resting’, which is usually expressed as a form of subtraction (e.g. ‘pain > resting’ or ‘pain – resting’). Such a contrasting approach is valid given that the assumption of pure insertion is true (Amaro Jr and Barker 2006). Under pure insertion, we assume that ‘pain processing’ is the only mental function that differs between ‘pain’ and ‘rest’ conditions. However, it is possible that something other than ‘pain’ is included in the contrast (Figure 2.5a). For example, subjects may pay greater attention during the pain‐stimulating condition but not the resting condition. In this case, the observed brain activation may represent not only pain processing but also increased attentional processing. The validity of the subtraction design would greatly influence how we interpret the behavioural meaning of observed brain activation.

2.2.5.2 Other Common Strategies of fMRI Design

The assumption of pure insertion is not always true because there may be more factors that interact with the mental function of our interest. To delineate the interaction between the factors, researchers may adopt a factorial design (Figure 2.5b). The design explicitly models more than one factor using multiple experimental conditions. For example, both attention to pain and intensity of pain stimuli are associated with pain processing. How do we delineate the association between brain activation and each of the factors (and their interaction)? As shown in Figure 2.5b, to delineate these effects, a factorial design with four conditions (mild/strong pain intensity × low/high attention of pain) can be designed. To investigate the brain activation associated with increased pain intensity, one can analyze the contrast ‘strong pain (with high and low attention)’ > ‘mild pain (with high and low attention)’. Notably, an interactional effect between the two can also be investigated. For example, the contrast [(strong pain–high attention > mild pain–high attention) > (strong pain–low attention > mild pain–low attention)] can be used to investigate the brain activation of increased pain potentiated by greater attention.

Another useful design is cognitive conjunction (Price and Friston 1997), which aims to identify the activation common to all experimental conditions rather than the distinct conditions. When there are multiple experimental conditions that share the same ‘basic’ mental functions (Figure 2.5c), it may be reasonable to find out an intersection between the patterns of brain activation derived from all these conditions (Amaro Jr and Barker 2006). For example, both the clenching task and the chewing task are associated with sensory feedback from the periodontium. Therefore, one may assume that the common pattern of brain activation may represent the processing of sensory feedback, which is common to both tasks (Figure 2.5c).

2.2.5.3 Considerations on the Statistical Threshold of Imaging Results

The control of errors is associated with the setting of the statistical threshold of the mapping results. In terms of neuroimaging findings, a Type I error means that one identifies an activation (which is above the statistical threshold), but the association between brain activation and mental functions only rises by chance. A Type II error means that one does not identify an activation (which is below a statistical threshold), but there exists a genuine association between brain activation and mental functions. The decision of setting a statistical threshold for imaging results is complicated by adopting ‘multiple tests’ in statistical analysis (Poldrack et al. 2008). As noted in the preceding sections, for both individual and group‐level analyses, statistical analyses are performed for each voxel separately. For each voxel, an alpha set at 0.05 would be reasonable for controlling the risk of a Type I error. However, because there are many voxels to be tested for statistical significance at the same time, multiple comparison would magnify the risk of Type I error if the alpha for every single voxel is set at 0.05. To reduce the risk of Type I error, researchers suggest adopting a threshold for controlling the familywise error or false discovery rate (Poldrack et al. 2008; Genovese et al. 2002), which helps to avoid identifying the voxels that survive the threshold merely by chance. However, one should also keep in mind that a threshold too strict may lead to increased risk in a Type II error. For example, brain activation associated with some mental functions, such as the activation induced by cognitive or affective manipulation, may have a smaller effect size (i.e. a smaller intensity, Figure 2.5c). These subtle but important differences may be missed if a stricter threshold is adopted (Lieberman and Cunningham 2009).

2.3.2.1 Biological Significance of Changes in Grey Matter

Grey matter predominantly consists of the cell body of a neural cell. Therefore, it is reasonable to consider that an increased volume of the grey matter reflects neurogenesis, i.e. an increased number of neurons (Zatorre et al. 2012). In adulthood, the formation of new neural cells has been identified in the dentate gyrus, and this neurogenesis can be associated with angiogenesis (Pereira et al. 2007). However, changes in grey matter may also be associated with synaptogenesis and more dendritic branching at the synapse of a neuron. In addition, even with the same number of neurons, changes in grey matter can be found when there is substantial sprouting of the neural axon, which reflects more connection between a neural cell with the others. Furthermore, the glial cells, including oligodendrocyte progenitor cells (OPCs) and astrocytes, can divide during adulthood. Changes in the brain features of grey matter may reflect an increased number of the glial cells or morphological changes of the cells (Zatorre et al. 2012).

2.3.2.2 Biological Significance of Changes in White Matter

There are several indices for quantifying changes in white matter, including white matter volume and fractional anisotropy (FA), an index mainly assessed using diffusion tensor imaging (DTI). An increased white matter volume may be associated with changes in the glial cells and angiogenesis (Zatorre et al. 2012). In contrast, FA may reflect the degree of the fibrous architecture, which has a profound effect on limiting the diffusion of water molecules. Therefore, an increased FA (i.e. the molecules move more ‘directionally’) can be found in a region with more fibrous structure.

2.3.3.1 What Does VBM Means?

In terms of neuroimaging, ‘morphometry’ can be considered an approach that measures the morphological metrics of the brain, including the size, shape and position of a part of the brain or the whole brain (Ashburner and Friston 2000). Conventionally, this can be carried out by selecting an anatomical structure of research interest (e.g. the thalamus) and having its border delineated by an expert manually. The size, shape and position of the selected structure can be assessed and compared between groups. When it comes to VBM, the measurement focuses on the voxel level rather than the anatomical structure as a whole (Ashburner and Friston 2000; Ashburner and Friston 2001). The brain images from two individuals are ‘matched’ at the voxel level, so the difference can be revealed. Such a process of ‘matching’ is achieved by registering the individual brain images to a template image. It should be noted that when two brains are matched at the voxel level, some morphological differences, such as the shape of individual brains, cannot be revealed because the shapes of individual brains have already been registered to the standard image, via multiple steps of transformation (Figure 2.3c). The VBM focuses on the intensity of each voxel, which may disclose important clues about the types of brain tissues, while discounting the individual difference in the global shape of the brain (Ashburner and Friston 2000, Ashburner and Friston 2001). For simplicity, VBM can be recognized as ‘a voxel‐based comparison of the local concentration of grey matter between two groups of subjects’ (Ashburner and Friston 2000). In other words, it is a method sensitive to the local composition of brain tissues, ‘while discounting positional and other large‐scale volumetric differences in gross anatomy’ (Ashburner and Friston 2001).

2.3.3.2 Steps of VBM Analysis

Practically, VBM is frequently performed on the T1‐weighted MRI data, which shows a good contrast between WM (with higher/brighter intensity), cerebrospinal fluid (CSF), with lower/darker intensity), and GM (with moderate intensity). Conventionally, the VBM approach consists of the following steps: (i) tissue classification, (ii) spatial normalization and (iii) intensity modulation.

The first key step is tissue classification. The original T1‐weighted image will be matched to tissue probability images. These images contain the information regarding the probabilistic information that a given tissue type (WM, GM or CSF) is found in the voxel (Ashburner and Friston 2005). The original T1‐weighted image will be segmented according to the probabilistic images. The segmentation generates three separate images that contain the GM, WM and CSF area, respectively (i.e. GM/WM/CSF‐segmentation images). Notably, in these segmented images, the area of a tissue type is not defined by a binary value, which represents the clearly‐cut border of the segmented part of the tissue. Instead, the voxel intensity of the segmented images ranges from 0 to 1, which represents the proportion of a tissue type within a voxel. Therefore, a voxel may have an intensity of 0.8 in the GM‐segmentation image and 0.2 in the WM‐segmentation image, suggesting it more likely to be classified as GM compared to WM. The second key step is spatial normalization. Back to the original concept of morphometry, if one needs to compare at the voxel level, an essential step is to match the individual brain images with each other. In VBM, this is achieved by spatial normalization, which registers the individual brain to a template image. Conventionally, VBM analysis uses a customized template, i.e. an ‘averaged brain’ estimated by the brain images from all the subjects included in the analysis. Individual images are registered to the template via linear and nonlinear transformation (see Section 2.2). Finally, the intensity of images is usually ‘modulated’ for estimating the volumetric information. During normalization, the local geometric features have been ‘morphed’ so that some areas may be contracted and some areas can be expanded. Notably, after the local deformation, the intensity value of each voxel will need further adjustment to compensate for the change of volumetric expansion/contraction. This adjustment is performed by ‘modulating’ the voxel intensity, which integrates the voxel intensity (based on tissue segmentation) and the information of local deformation (Jenkinson and Chappell 2018).

2.3.3.3 Interpretation of the VBM Results

As noted in the preceding section, in the GM image derived from segmentation, the voxel value should be realized in a probability sense, i.e. how possible this voxel can be classified as part of grey matter. Therefore, this value does not quantify the ‘actual size’ of grey matter tissue. The VBM results consider both the results of tissue classification (e.g. the amount of GM) and the volume change (i.e. spatial normalization). Therefore, the results can be considered ‘the proportion of voxel that is grey matter, having adjusted for the confounding effects of warping the brains’, or from the perspective of volumetric change, as ‘the proportion of volume change attributable to grey matter’ (Ashburner and Friston 2001). Some interpretations of VBM results can be over‐simplified and misleading. For example, when a VBM analysis revealed a smaller grey matter volume of the hippocampus in patients with dementia, compared to healthy controls, the results should not be interpreted as a smaller hippocampal size because it ignores the fact that the volume change is adjusted from specific tissue type (here, for the grey matter).

2.3.4.1 Assessment of Cortical Thickness

The cortex is mainly composed of grey matter, which forms continuous layers folded into multiple gyral and sulcal regions. One of the primary morphological features of the layer structure is its thickness. In the surface‐based approach, such as the method based on FreeSurfer (Fischl 2012), the thickness of the cortical layer (i.e. cortical thickness) is defined as the distance between the grey/white and pial surfaces. The surface‐based methods have been proved to be a useful way of studying cortical thickness. For example, Fischl and Dale (2000) have investigated the thickness of the cerebral cortex from 30 younger adults, showing an average ± standard deviation thickness of 2.7 ± 0.3 mm in the gyral area and 2.2 ± 0.3 mm in the sulcal area. In general, the cortical thickness is within the range of 1– 4.5 mm, consistent with the findings from post‐mortem research (Fischl and Dale 2000). The thickness‐based analysis has provided useful information for our understanding of the brain. Firstly, the analysis considers the realistic shape of the brain cortex, which is full of folding areas. Secondly, the analysis is also used for assessing other surface features, including sulcal depth (as an index for the boundary between brain lobes) and curvature (i.e. how curved or flat the part of the surface is), in addition to cortical thickness. Thirdly, the analysis may also help to match images between individual subjects. For example, across subjects, the structural images can be normalized to a template by matching the position of sulci, which may provide more accurate registration of brain images between different individuals.

2.3.4.2 Segmentation of Brain Regions

As noted earlier, segmenting different types of brain tissues is a critical step for analyzing the structural features of the brain. This tissue segmentation can be performed decently by VBM. However, segmenting different brain structures, i.e. to label a voxel as part of the hippocampus or the amygdala, can be a real challenge because this classification cannot be carried out merely by assessing the intensity of a voxel. To achieve this, researchers have adopted positional information from the brain, using a similar concept as surface‐based analysis. In addition to assessing the information of voxel intensity, the relative spatial location of brain structures is considered in the algorithm of segmentation (Fischl 2012). For example, a voxel will show a greater probability of being classified as the amygdala than the hippocampus if its spatial location is in front of a voxel classified as part of the hippocampus (based on the a priori knowledge that the amygdala is anatomically anterior to the hippocampus). The surface‐based approach, such as the method based on FreeSurfer, has been widely used for the automatic segmentation of cortical and subcortical regions and the estimation of their volumes.

2.3.4.3 Steps of Surface‐based Approach

The general step of the surface‐based analysis is similar to VBM analysis, in which segmentation and spatial normalization play a key role. An obvious difference between VBM and the surface‐based approach is the method for image registration. In VBM, the individual brain images are registered to a template image, which is positioned in a 3D space composed of orthogonal axes in three directions. In the surface‐based approach, the registration is performed in a ‘surface space’, which can be visualized as a inflated spheric area that represents the whole surface area of the cortex. The ‘surface space’ is different from the ‘voxel space’ of VBM analyses. In VBM, brain voxels are organized in a fixed grid with three dimensions. In contrast, the surface space is organized as a mesh composed of multiple small triangles (i.e. faces) with intersected points (i.e. vertices). Notably, while the number of voxels is fixed in VBM (based on its spatial resolution), the number of vertices of the mesh is not fixed and needs to be estimated to fit the individual brain (Jenkinson and Chappell 2018). The different ways of organization of brain images have a profound influence on how data are analyzed.

Before registration, the original brain image needs to be transformed into this surface area by mapping the x‐, y‐ and z‐coordinates from the ‘brain space’ to the surface space. This is performed by an algorithm that deforms the folded brain (with a lot of sulci) into an inflated sphere, much like blowing air to a crumpled plastic bag to inflate it like a balloon. By this deformation, the locational information of the sulci and gyrus can be transformed into a smoother surface for analysis (Jenkinson and Chappell 2018). The template to be registered is also represented in the surface space, and therefore, within the same surface space, individual brain images are normalized to the template. Notably, because the 3D gyral and sulcal regions are ‘flattened’ into a surface form, many morphological features, including the surface area of cortical regions, can be analyzed via this approach.

2.3.5.1 Assessment of Microstructure of White Matter

dMRI assesses the features of molecular diffusion from multiple directions and the attenuation of magnetic resonance signal associated with the molecules spinning. Therefore, when signal attenuation is more pronounced in one direction than directions, it signifies that in this particular direction, molecules can diffuse more freely compared to the other directions. In DTI, axial diffusivity (AD) is the diffusivity assessed along the long axis. Diffusivity is also assessed along the direction perpendicular to the axial direction, i.e. the radial diffusivity (RD). The mean diffusivity (MD) is the average of diffusion over all directions. The FA represents the degree that the estimated pattern of diffusion deviates from an isotropic form. The higher the FA value is, the more likely that diffusion is restricted in a single direction (i.e. anisotropic) rather than spread evenly in all directions. It is noteworthy that the local properties only reflect the molecular behaviour of diffusion, they cannot be overdrawn as an index of white matter integrity (which should be preserved in a pathological condition), and the changes in the local properties cannot be directly translated to the changes in structural connectivity (Jones et al. 2013).

2.3.5.2 Tractography: Estimation of Anatomical Connectivity

In addition, dMRI is also a powerful tool for researchers to explore the global architecture of the brain by answering questions such as ‘which gray matter regions are inter‐connected by white matter fibers?’ (Jones et al. 2013). To investigate the structural connectivity between brain regions, one would adopt the approach tractography, an analysis ‘to determine anatomical connectivity by tracing the paths of axonal fiber bundles through the white matter’ (Jenkinson and Chappell 2018). It should be noted that tractography is the method primarily for qualitatively visualizing the connection between grey matter regions based on the local properties of molecular diffusion. One needs to be careful when using the results of tractography for quantitative use, such as to identify the ‘number of fibres existing’ between brain regions. As shown in Section 2.4, the link between the streamlines estimated by tractography and the real ‘axonal fibres’ should not be simplified because the streamlines are estimated based on the properties of local diffusion, and the estimation per se is influenced by many factors, such as the density of fibres in a voxel and the length and shapes of fibres, which cannot be easily resolved by the dMRI data (Jones et al. 2013).

2.4.3.1 Intrinsic Brain Functions

As noted earlier, functional connectivity can be used to quantify the functional signals collected during a resting state, in which subjects are not engaged in a task. Why is it important to explore the connectivity during a resting rather than a task condition? To explain this, one needs to consider the intrinsic brain functions, which are less related to the sensory and motor functions induced by a specific task. In other words, some brain functions are associated with the ‘baseline status’ (i.e. the non‐task‐specific conditions) of our mind. These functions include information processing for ‘interpreting, responding to and predicting environmental demands’ (Raichle 2010). Experimentally, this baseline status is set by asking subjects to relax and rest during fMRI scanning. The importance of the baseline status can be demonstrated by the fact that the brain, with only 2% of our body weight, consumes around 20% of the total energy during resting (Raichle 2010). Notably, even when the brain is actively engaged with a mental operation (e.g. performing a language task), the additional energy consumption is often less than 5% (Raichle 2010). The findings of the high baseline consumption of energy suggest that even when we are not engaged with a mental function overtly, the brain always maintains intrinsic and ongoing activities.

2.4.3.2 Spontaneous BOLD Activity and the Resting‐state fMRI

In terms of the connectivity of intrinsic brain functions, researchers focus on the temporal correlation of the spontaneous BOLD activity, a low‐frequency signal (0.01–0.1 Hz) collected during a resting state. The spontaneous BOLD activity can be defined as ‘the activity that is not attributable to specific inputs or outputs’ (Fox and Raichle 2007). Therefore, the activity is usually assessed in a resting state when subjects are not actively engaged with a specific sensory or motor task. The fluctuation of this BOLD activity may represent the stimulus‐independent mental activity, such as self‐referential processing or memory, which are considered part of intrinsic brain function (Fox and Raichle 2007; Raichle 2010). It may also represent a preparatory status for coming tasks by coupling the brain regions that usually work together for a specific function (Fox and Raichle 2007, Raichle 2010).

2.4.3.3 Research Approaches of Functional Connectivity

Cumulating evidence has revealed that even during the resting state when individuals are not actively engaged with external stimuli, the human brain still works actively, as demonstrated by the connectivity of the spontaneous BOLD activity. The study design of intrinsic functional connectivity is illustrated in Figure 2.7. Firstly, the spontaneous BOLD activity is acquired during a resting state, which relates to the intrinsic brain functions of a non‐task‐specific ‘baseline’ status (Figure 2.7a). The brain is segmented into multiple brain regions according to a brain atlas (Figure 2.7b) (see Box 2.4 in the Companion Website). For an individual brain region, BOLD time series is extracted from each of the voxels within the brain region, and a mean time series of a region is calculated by averaging the BOLD time series of all the voxels (Figure 2.7c). Several additional steps are included here, such as extracting the low‐frequency component of the time series. Next, based on the definition of functional connectivity, the strength of association between the brain regions is quantified by correlation coefficients (Figure 2.7d). The correlation coefficient represents the strength of the connection between each pair of brain regions (Figure 2.7e). For example, a stronger correlation is identified between region 1 and region 2, compared to the correlation between region 2 and region 4. The approach is helpful to elucidate a hypothesis based on a priori knowledge of neural circuitry. For example, one can compare the strength of functional connectivity between two plausible pathways (e.g. between region 1 and region 2 or between region 2 and region 4). One can also use the same approach for investigating individual differences in behaviour, such as quantifying the association between perceived pain and the connectivity of pain‐related regions.

Another widely used approach is the seed‐based approach. The approach explores the brain regions that are highly correlated with a ‘seed’ region at the voxel level. For the seed‐based approach, the BOLD time series from a pre‐defined brain region (i.e. the ‘seed region’) is collected, and correlation is calculated between the time series of the seed region and the time series from all the voxels outside the seed region (Figure 2.7f). This step will generate a functional connectivity map, which reveals the area with stronger connectivity with the seed region. The seed‐based approach is especially useful to explore the global pattern of brain regions that form strong functional connectivity with the region of our interest (i.e. the seed).

2.4.4.1 Structural Connectivity Based on Tractography

dMRI provides information regarding the local properties of molecular diffusion at the voxel level (see Section 2.3). Based on the dMRI data, tractography can be used to reveal the streamlines connecting brain regions. Structural connectivity is quantified according to the ‘streamlines’ estimated using the algorithm of deterministic tractography or probabilistic tractography. In deterministic tractography, each voxel is assigned with a single direction (Figure 2.8a), and a continuous curve (i.e., a streamline) is formed by tracking the direction of voxels (Jenkinson and Chappell 2018). In probabilistic tractography, there exists an uncertainty of the direction within a voxel. Therefore, the direction of a voxel may vary, forming a probability distribution. As shown by a simplified case in Figure 2.8b, the distribution presents a high probability for the leftward direction. However, it does not exclude the possibility of an upper direction, though the probability is smaller. Due to the probabilistic nature of voxel direction, it may not be adequate to track for a single streamline. Instead, tracking procedures are repeated many times, and different streamlines with random directions can be identified (Figure 2.8b) (Jenkinson and Chappell 2018). As shown in Figure 2.8b, probabilistic tractography reveals the tract consisting of the most likely direction from individual voxels. The intensity of a voxel represents the frequency that a streamline passes that voxel under a fixed number of sampling (of the streamlines). Therefore, a higher intensity suggests that it is more likely to find a streamline passing the voxel.

2.4.4.2 Structural Covariance

Structural covariance refers to the phenomenon that ‘inter‐individual differences in the structure of a brain region often covary with inter‐individual differences in other brain regions’ (Alexander‐Bloch et al. 2013). Simply speaking, in a group of subjects, two regions are structurally covaried if their structural features (such as cortical thickness) are highly correlated across the subjects. Notably, the concept of structural covariation is established on the group level. The covariation reflects the association of inter‐individual differences in structural features. Therefore, the first step of calculating structural covariation is to quantify the structural features across the subjects, such as assessing the average cortical thickness from brain regions. The degree of covariation can be quantified by the correlation coefficient between the regional cortical thickness across all the subjects (Figure 2.8c). The biological mechanisms underlying structural covariance have not been fully elucidated. The pattern of inter‐regional association revealed by structural covariance shows a substantial degree of overlap with the pattern from intrinsic functional connectivity (Kelly et al. 2012b) and the structural connectivity based on diffusion connections (Gong et al. 2012). The brain regions covary in structural features may share coordinated rates of developmental process (Alexander‐Bloch et al. 2013).

2.4.5.1 The Definition of a Node

In the graph‐based network analysis, the definition of nodes is the most fundamental issue. A node can be conceived as the elemental unit to define a brain region. The links between brain regions (e.g. the inter‐regional correlation of the BOLD time series) can be quantified only when we have defined what a brain region is. For example, the node can be a brain structure with a clear anatomical border, such as the thalamus and the amygdala, and functional connectivity is quantified as the correlation between average BOLD time series from all the voxels within each region. It can even be a single voxel, and functional connectivity will be quantified between all the pair‐wise BOLD time series from all the voxels. The definition of nodes is sometimes associated with the ‘resolution’ of the brain network. A network may consist of around 100 nodes, each defined as a structurally or a functionally distinct region. In contrast, a network may consist of more than 10 000 nodes when a node is defined at the voxel level. To elucidate how nodes are defined is essential to interpret the meaning of a network properly (Butts 2009). For example, not all the ‘brain regions’ are structurally or functionally well defined as the thalamus or the amygdala. The border of some regions, such as the dorsolateral prefrontal cortex, may show great inter‐subject variability. For structural connectivity, one may define the region based on some anatomical landmarks (e.g. gyri and sulci). However, the same definition may not reflect the same brain functions across subjects. For example, it may be invalid to claim that the same area of the dorsolateral prefrontal cortex is ‘the node for attention control’ to all subjects. Secondly, back to the problem of the resolution of a network, we need to consider how a structure should be defined as a functionally distinct unit. For example, it seems reasonable to define the thalamus and the amygdala as different nodes because they are associated with sensorimotor and cognitive–affective processing, respectively. However, in the thalamus, different sub‐nuclei (e.g. the ventromedial or lateral nuclei) are associated with different roles in sensorimotor processing. Should we include the whole thalamus as a node? Or should each of the sub‐nuclei be investigated as an individual node? This will lead to different biological interpretations of a brain network.

2.4.5.2 The Definition of a Link

As noted above, the link between nodes can be quantified using different indices of functional or structural connectivity. However, different background settings of analysis will have a great impact on the resulting connectivity. For example, if we define the correlation between the BOLD time series as the link in a network of functional connectivity, we may find both positive and negative correlations within all the pairs of nodes. What is the biological meaning of the ‘negative connectivity’ (i.e. a link with a negative correlation coefficient)? Should we include the results of negative connectivity or exclude them so that only the links with positive connectivity are investigated? A network with both negative and positive connectivity and a network composed of only positive connectivity should be interpreted differently. Another analytical issue is the binarization of the value of a link. On the one hand, we may binarize the value of correlation as 0 or 1 (i.e. to classify a link as ‘presence’ vs. ‘absence’) by a pre‐defined threshold. On the other hand, we may keep the value to form in a weighted network so that the strength of connectivity can be treated as a continuous variable. The issues highlight the fact that the results of network analysis are sensitive to the analytical steps of defining a link (Murphy and Fox 2017).

2.4.6.1 Global Metrics

Characteristic path length (PL) and global efficiency (GE) are two widely used metrics to quantify the degree of integration of a network (Rubinov and Sporns 2010) (Figure 2.9b). PL is the average ‘shortest path length’ between all pairs of nodes. A smaller value of PL means averagely fewer ‘steps’ to pass through between each pair of nodes. The GE, in contrast, is calculated based on the inverse PL. Therefore, a network with a shorter PL and a higher GE reflects the better efficiency of integrating information between nodes. Notably, GE or PL is also the major feature for evaluating if a network demonstrates a ‘small‐world’ architecture (Figure 2.9b). A ‘small‐world network’ is both highly integrated and segregated – it is more clustered than random networks (i.e. increased segregation) while preserving short PL, compared to regular networks (i.e. increased integration) (Watts and Strogatz 1998). Based on the analysis of PL and GE, researchers have identified that the structural and functional networks of the human brain also demonstrate a small‐world architecture (Bassett and Bullmore 2017).

2.4.6.2 Local Metrics

While PL and GE contribute to assessing the degree of function integration, the metrics of clustering are helpful to quantify the degree of functional segregation. One of the simplest forms of ‘clustering’ of nodes is to form a triangular connection (Figure 2.9c), in which all three nodes fully connect. Clustering coefficient (CC) is used to quantify the fraction of the triangular architecture in the whole network. A higher CC represents that the pattern of clustered nodes is more prevalent in a network (Rubinov and Sporns 2010). Another common index for segregation is modularity, which reflects the degree that a network is organized into a modular architecture, which consists of multiple ‘modules’ (or communities). A module can be generally defined as a group of nodes sharing a high degree of within‐group connectivity and, at the same time, a low degree of between‐group connectivity (Rubinov and Sporns 2010). Just like the small‐world architecture, being modular is also a key feature of the functional or the structural network of the brain (Bassett and Bullmore 2017).

2.4.7.1 Confounding Factors of Analyzing Functional Connectivity

Several factors may confound the findings of intrinsic functional connectivity. Firstly, the functional signals acquired during a resting state are associated with not only our baseline mental functions but also individual physiological processes (Kelly et al. 2012a; Murphy et al. 2013). It is estimated that 5–15% of the variance in intrinsic BOLD activity is accounted for by cardiac and respiratory processes (Kelly et al. 2012a). Therefore, individual differences in these physiological processes, which are especially pronounced in patients with systemic diseases, should be carefully evaluated when we interpret the results of functional connectivity. Secondly, head motion has a substantial impact on the results of functional connectivity analyses (Van Dijk et al. 2012). The effect of head motion may vary in different brain regions. Increased head motion is associated with stronger intrinsic functional connectivity of motor network but weaker connectivity of the default mode and frontoparietal networks (Van Dijk et al. 2012). Critically, the degree of head motion may differ between different groups of individuals, such as younger and older subjects. Therefore, the age factor should be carefully considered when one compares the pattern of connectivity between different groups. Thirdly, one issue that has been debated for years is the use of global signal regression, an analytical step to remove the global mean BOLD signal, which may be unrelated to neural activity (Murphy et al. 2013). However, the adoption of this step is associated with an increased proportion of negative connectivity in the functional network (i.e. more links with anti‐correlation between the BOLD time series), which may greatly influence how we interpret the results (Murphy and Fox 2017).

2.4.7.2 Misinterpretation of Findings of Structural Connectivity

A common myth of interpreting the local properties of molecular diffusion is that ‘if there is a greater FA in a voxel, there are more neural fibres’. Such a direct translation between the imaging findings at the voxel level and the biological features of neural fibres is not valid. Even for the findings of tractography, we need to keep in mind that some biological features, such as the size, shape and length of neural fibres, cannot be directly assessed from tractography (Jones et al. 2013). Therefore, one should be careful of generalizing the results of structural connectivity into clinical conditions. For example, a claim that ‘individuals show loss of white matter integrity’ merely based on a change of FA or MD value should be revisited cautiously (Jones et al. 2013). Similarly, the ‘tracts’ demonstrated by tractography merely reflect the pattern of streamlines passing through different brain regions. The neuroanatomical features of neural fibres need to be confirmed by other methods, such as tract‐tracing methods based on neurochemical agents.

2.4.7.3 Methodological Variations of Graph‐based Analyses

As shown previously, graph‐based network analysis is a powerful tool for quantifying some topological metrics, which help us to understand the pattern of integration/segregation of brain networks. However, we should keep in mind that all the metrics are calculated based on the network. Therefore, it is critical to evaluate if the definitions of nodes and links represent the biological architecture of our brain. Specifically, the nodes of the brain network should represent a single entity that takes part in the relation of a network, and the links should reflect the biological meaning of the relations (Butts 2009). In the literature of graph‐based analysis of brain networks, there exists a great methodological variation in defining nodes and links for brain networks. Many studies defined the nodes based on structural features, which can be reliably reproduced between subjects. However, structural boundaries of different parts of the brain cannot be equated to their functional boundaries (Smith 2012). An alternative method is to define a functional region according to the map of brain activation derived from task‐based research (Fornito et al. 2013) (see Section 2.2). However, the size/location of these functional regions still show a substantial variability between subjects. The variability would be pronounced when it comes to mental functions regarding cognitive–affective processing, which usually shows a great variation in the location and size of task‐based brain activation.

The methods for defining links also exist with a great variation. One of the key issues is the use of a threshold on the value of a link. When a threshold is applied on a network, a link will be preserved if its value is above the threshold, and it will be removed if its value is below the threshold. In other words, after thresholding, only links of stronger connectivity will be preserved for graph‐based analysis. The criteria for an ‘optimal’ threshold are still under debate (Fornito et al. 2013; Smith 2012). If the threshold is too high (i.e. only the links of very strong connectivity will be preserved), the network will become very sparse, and the sparsity may influence the topological metrics. In general, one should interpret the results of brain networks only when the analytical methods of network analysis are elucidated.

2.4.8.1 What Does ‘Resting‐state’ Function Connectivity Represent?

The term ‘resting state’ may give a false impression that subjects are ‘doing nothing’ during the scan. The meaning of ‘resting’ should be interpreted relative to a task condition. A resting state means subjects are less actively engaged with external stimuli or complex mental processing, i.e. a non‐task‐specific condition. It does not mean the brain is totally shut down – since the brain is always active (Raichle 2010). Even during a resting state, some essential mental functions are maintained for responding to environmental demands. Again, because individuals are not engaged with an explicit task in the resting state, it would be difficult to interpret the behavioural meaning of intrinsic functional connectivity. Behavioural/clinical variables of individual subjects should be carefully collected to clarify the association between intrinsic functional connectivity and individual variations in behavioural/clinical aspects.